Sense and sign in wave and crystal dislocations

Abstract

Dislocations in waves and in crystals are compared, in tutorial style, withparticular emphasis on signs and senses. Reconnection of dislocations and thedisappearance of a closed loop are treated as examples. There is a fundamentaldifference between the regularized phase gradient of a wave dislocation or wavevortex, as defined in a recent paper, and the Burgers vector of a dislocation in acrystal; the latter, as is well known, is not strictly a vector at all, because, todefine it, a sense of direction for the dislocation line has to be chosen arbitrarily.The Burgers vector in a crystal is more analogous to the phase circulation of ± 2π around a wave dislocation. The new vector now associated with a wave dislocation could becalled, not the Burgers vector, but simply ‘the phase gradient vector’. A new result is to seethat, by an isotropic scaling, two parallel straight dislocation lines of opposite sign haveidentical phase patterns in the plane normal to them, regardless of whether they are of pureedge, or mixed edge/screw type.